You should let React render everything, and your job is only to tell React what to render and, in your case, how many times. For that, a counter
can be used to track how many dynamically-added should be "injected" inside the <Example>
component.
A mindshift is needed here, since in your example you are coming from a place where you think that the click handler itself should modify the DOM, and in React that is an antipattern.
Instead, you should work with state, and that means the click handler should update the state of the host component and that will trigger a re-render (this is how React works) and in the next render cycle, your added component will be rendered as many times as the counter value, because that counter change is what triggered the re-rendering.
In React, the props & state are the way to trigger re-render and any DOM modification should be done by changing the internal component's state, or by sending different props, from the parent component.
In the below example I do not use Classes, but use Hooks instead, because I've stopped using class altogether once hooks were released, because I think it's cleaner:
const {useState, Fragment} = React
// The added element component
const AddedElement = () => <p><input placeholder='text box' /></p>
// The parent component
const App = () => {
const [count, setCount] = useState(0) // Name it however you wish
return <Fragment>
<button onClick={() => setCount(count + 1)}>Click me</button>
{ [...Array(count)].map((_, i) => <AddedElement key={i} />) }
</Fragment>
}
// Render
ReactDOM.render(<App />, document.getElementById("react"))
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/16.11.0/umd/react.production.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/16.11.0/umd/react-dom.production.min.js"></script>
<div id="react"></div>
If you are interested in how to repeatedly render the same component, I've written an answer about this in this question: How can I render repeating React elements?